# 4.1.6. Comt: comptonisation model¶

This is the model for Comptonisation of soft photons in a hot plasma, developed by Titarchuk (1994). See the XSPEC manual for more details. The code was substantially improved and brought to the SPEX standards.

## 4.1.6.1. Some modifications¶

Titarchuk (1994) gives an analytical approximation for ) to the exact calculations as provided by Sunyaev & Titarchuk (1985) for . Their approximation has the proper asymptotic behaviour for small and large values of , but unfortunately has deviations up to 7 % over the range for . The approximation by Titarchuk is given in their equations (27) and (28) by

We found an approximation that is better than 1 % using a slight modification of the above equations. We use these new approximations in our calculations:

Warning

For the physically valid range of parameters, consult the XSPEC manual; see also Hua & Titarchuk (1995), their Fig. 7.

The parameters of the model are:

`norm`

: Normalisation of the power law, in units of
. Due to the way the model is calculated, this is not
the flux at 1 keV! Default value: 1.`t0`

: The temperature of the seed photons in keV. Default
value: 1 keV.`t1`

: The plasma temperature in keV. Default value: 100
keV.`tau`

: The optical depth. Default value: 3.`type`

: The type of geometry. Allowed values are 0 for a disk
(default) or 1 for a sphere. This is a frozen parameter (cannot be
fitted).*Recommended citation:* Titarchuk (1994)